Laurent Polynomial

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form

where the a_i are elements of F, and only finitely many of the a_i are nonzero. A Laurent polynomial is an algebraic object in the sense that it is treated as a polynomial except that the indeterminant "t" can also have negative powers.

Expressed more precisely, the collection of Laurent polynomials with coefficients in a field F form a ring, denoted F[t,t^(-1)], with ring operations given by componentwise addition and multiplication according to the relation

for all n and m in the integers. Formally, this is equivalent to saying that F[t,t^(-1)] is the group ring of the integers and the field F. This corresponds to F[t] (the polynomial ring in one variable for F) being the group ring or monoid ring for the monoid of natural numbers and the field F.

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References

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Cite this as:

Weisstein, Eric W. "Laurent Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LaurentPolynomial.html

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